SOVIET ATOMIC ENERGY VOL. 46, NO. 1

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• Release Decision: RIFPUB
• Original Classification: K
• Document Page Count: 86
• Document Creation Date: December 23, 2016
• Document Release Date: February 12, 2013
• Sequence Number: 1
• Publication Date: January 1, 1979
• Content Type: REPORT

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Russian Original Vol. 46, No. 1, January, 1979
July, 1979
SATEAZ 46(1) 1-8e (179)
_
SOVIET
ATOMIC
ENERGY
ATOMHAH 3HEPrt1fi
(ATOMNAYA ENERGIYA)
TRANSLATED 'FROM RUSSIAN
CONSULTANTS BUREAU NEW YORK
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T-31
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SOVIET Soviet, Atomic Energy is a cover-to-cover translation of Atomnaya
Energiya, a publication of the Academy of Sciences of the USSR.
ATOMIC
ENERGY
r
,
Soviet Atomic Energy is abstracted or in-
dexed in Applied Mechanics?ReviAvs, Chem-
ical Abstracts, Engineering Index, INSPEC?
Physks Abstracts and Electrical and Elec-
tronics Abstracts, Current Contents, and
Science Abstracts.
An agreement with the Copyright Agency of the USSR (VAAP)
makes available both advance copies, of the Russian journal and
original glossy photographs and artwork. This serves to decrease
the necessary time lag between publication of the original and'
publication Of the translation and helps to iinprove the quality
of the latter.: The translation began with the first issue Of the
Russian journal .-
Editorial Board of Atomneya Energiya:
Editor: 0: D. Kazachkovskii,
Associate Editors: N. A. Vlasov and N. N. Ponomarev-Stepnoi
?
I. N. Golovin V. V. Matveev
V. I. ll'ichey I. D. Moroktiov
V. E. Ivanov A. A.,NaCimov
V. F. Kalinin A. S. Nikiforov
P. L. Kirilov A. S. Shtan'
Yu. I. Koryakin B. A. Sidorenko
A. K. Krasin - M. F. Troyanov
E. V. Kulov E. I. Vorob'ev
- B. N: Laskorin
Copyright 0 1979, Plenum Publishing.Corporation. Soviet Atomic Energy partici- -
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SOVIET ATOMIC ENERGY
A translation of Atomnaya Energiya
July, 1979
Volume 46, Number 1
January, 1979
CONTENTS
ARTICLES
Technicoeconomic Aspects of the Realization of Centralized Heat Supply
from Atomic Boiler Units ? I. Ya. Emel'yanov, B. B. Baturov,
V. P. Korytnikov, Yu. I. Koryakin, V. A. Chernyaev, Ya. A. Kovylyanskii,
Engl./Russ.
and I. V. Galaktionov
1
3
Multicriterial Optimization of the Development of Nuclear Power
in the Framework of the Perspectives of COMECON
? V. N. Bobolovich and N. A. Trekhova
7
9
An Estimate of the Uncertainty Factor for Predictingthe Development
of Nuclear Power Engineering ? S. Ya. Chernavskii
12
13
Method of Computing Large Perturbations of Reactivity by Difference
Iterations in the Monte Carlo Method ? V. B. Polevoi
18
20
Corrosion Products in Main Technological Systems of Atomic
Power Plants with an RBMK-1000 Reactor during Operation
? V. M. Sedov, P. G. Krutikov, E. A. Konstantinov,
A. V. Shul'gin, V. I. Ryabov, Yu. 0. Zakharzhevskii,
A. P. Eperin, and V. G. Sheychenko
22
23
M8ssbauer Spectroscopic Determination of Phase Composition
of Corrosion Products of Structural Materials of Primary
Circuit of RBMK-1000 Reactor with Neutral Water Conditions
? L. N. Moskvin, A. A. Efimov, I. A. Varovin, G. A. Usacheva,
S. B. Tomilov, and A. A. Petrov
27
28
Activity of Radionuclides in the Coolant of the Secondary Loop of a Nuclear
Power Plant with VVER-440 Reactors ? L. M. Voronin, A. P. Volkov,
V. F. Kozlov, L. M. Luzanova, and V.1. Pashevich
31
31
24P
Measurement of the ?u/235U and 242Pu/235U Fission Cross-Section
Ratios for 0.127-7.4-MeV Neutrons ? V. M. Kupriyanov, B. I. Fursov,
B. K. Maslennikov, V. M. Surin, and G. N. Smirenkin
35
35
Estimates of Global 85Kr Radiation Safety ? I. Ya. Vasilenko, Yu. I. Moskalev,
and A. G. Istomina
39
40
LETTERS
Contact Conductivity between a UO2 Core and Cladding ? B. V. Samsonov
and S. V. Seredkin
44
45
Spatial Distribution of Slow Hydrogen and Helium Atoms Introduced
in a Solid ? A. F. Akkerman
47
47
Algorithm to Estimate the Local Perturbations of Linear Radiation-Flux
Functionals Using the Monte Carlo Method ? V. B. Polevoi
50
49
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CONTENTS
(continued)
Engl./Russ.
Porosity Distribution in Nickel Following Argon Bombardment
?S. Ya. Lebedev and S. I. Rudnev
53
51
135mBa Yields 1n133Cs(a, pn)135mBa and 133La(p,an)135mBa Nuclear Reactions
? P. P. Dmitriev and M. V. Panarin
55
53
Parameters of "Co Neutron Levels ? V. A. Anufriev, S. I. Babich,
A. G. Kolesov, V. N. Nefedov, V. V. Tikhomirov, V. S. Artamonov,
R. I. Ivanov, and S. M. Kalebin
57
54
Tests on Zirconium Superheating Channels in the First Unit at the Kurchatov
? Beloyarsk Nuclear Power Station ? A. N. Grigor'yants, B. B. Baturov,
V. M. Malyshev, S. V. Shirokov, and V. I. Mikhan
58
55
In Memory of Yurii Aronovich Zysin
61
57
COME CON CHRONICLES
Collaboration Diary
63
59
INTERNATIONAL COOPERATION
Meeting of the Working Grow on Power Engineering ? M. B. Agranovich
66.
61
CONFERENCES AND SEMINARS
Conference on the 30th Anniversary of Isotope Production and Use
In the USSR ? A. K. Kruglov and N. A. Matyushina
67
61
Seminar on Reactor Engineering ? R. R. Ionaitis
69
63
IAEA Conference on Leak Detection in Fast-Reactor Steam Generators
? A. S. Mavrin
72
65
Sixth International Conference on Heat Exchange ? V. S. Osmachkin
74
66
Seventh International IAEA Conference on Plasma Physics and Controlled
Thermonuclear Synthesis ? V. S. Mukhovatov?
76
68
Symposium on High-Current Pulse Electronics ? G. A. Mesyats
and E. B. Yankelevich
78
70
The Russian press date (podpisano k pechati) of this issue was 12/25/1978.
Publication therefore did not occur prior to this date, but must be assumed
to have taken place reasonably soon thereafter.
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ARTICLES
TECHNOECONOMIC ASPECTS OF THE REALIZATION
OF CENTRALIZED HEAT SUPPLY
FROM ATOMIC BOILER UNITS
I. Ya. Emel'yanov, B. B. Baturov,
V. P. Korytnikov, Yu. I. Koryakin,
V. A. Chernyaev, Ya. A. Kovylyanskii,
and I. V. Galaktionov
UDC 658.26:621.311.2
It is now quite clear that it is desirable and necessary to widen the sphere of application of nuclear en-
ergy resources, with primary emphasis being given to the use of nuclear reactors for residential community
and industrial heat supply. This is due to the fact that out of the total quantity of fuel used, 30-460 of fuel re-
sources are devoted to the needs of heat supply, 50% more than is used for producing electrical power.
While electrical power is generated mainly by burning low-grade coal, the requirements of heat supply are
met mainly by high-quality gas fuel.
Experience in operating atomic central heating-and-power plants (ACHPP) (Bilibinsk in the USSR and
"Agestan in Sweden) shows without a doubt that it is technically possible to construct radiation-safe and opera-
tionally reliable nuclear sources of heat supply. Studies have now been completed [1-3] which have determined
the principles of organization and the conditions needed to ensure economic efficiency of centralized heat supply
on the basis of ACHPP. These questions have not yet been nearly as thoroughly analyzed in their application
to atomic boiler units (ABU).
Principles of the Organization and Application of Organic-Fuel Boiler Units. In spite of the well-known
advantages to be gained by combining the production of heat and electrical energy with central heating-and-
power plants (CHPP) (these are becoming more widely used with the improvement of the central-heating en-
ergy cycle), heat supply from boiler units using organic fuel has been widely developed because of several
reasons. The main reason is that raising the coefficient of centralization of the heat supply is made possible
by the economic efficiency gained when heat from a common source is supplied to relatively small users, for
whom heat supply by CHPP is economically undesirable or impossible because of:
a low level of the total heat loads of individual cities, residential communities, and industrial enterprises,
resulting in a reduction of the unit output of CHPP energy units and the deterioration of their technico-
economic indicators;
a low territorial density of heat usage in a given region, resulting in highly capital-intensive heat sys-
tems with large amounts of waste when incorporation of users is pushed to the level of total heat load
appropriate to CHPP operation;
the impossibility of locating CHPP's in a given region because water resources are lacking, or there
are no areas suitable for construction (e.g., in the center of large cities).
Table 1 gives data which illustrate the importance of a centralized heat supply for relatively small heat
users relative to the fuel and energy economy of our country. Table 1 shows the structure of the concentra-
tion of heat loads and the shares of various levels of concentration in the total rate of fuel consumption of the
country [4].
The use of regional boiler units (RBU) as a means of supply is economically efficient for small heat
users due to the specific characteristics of the former as sources of centralized heat supply;
the relative simplicity of their main equipment compared with CHPP and their resulting far lower spe-
cific cost for small attached heat loads (the capital component of the cost and of the specific reduced expendi-
tures when heat is produced by boiler units is 5-15%);
Translated from Atomnaya Energiya, Vol. 46, No. 1, pp. 3-9, January, 1979. Original article submitted
June 5, 1978.
0038-531X/79/4601-0001 $07.50 ? 1979 Plenum Publishing Corporation 1
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TABLE 1. Illustrative Characteristics of Heat Load Concentration
in the USSR
1970
Growth since 1971
No. of
total heat
No. of
total heat
No. of
total heat
Mean heat loadsload
of cities, Gcal/h
cities
load
cities
cities'
load
Tcal/h
%
Tcal/h
%
Tcal/h,
%
>10
9
40
14
f
301
10
3
70
12
5-10
3
20
7
1.4
95
32
17
115
20
3-5
17
65
23
12
45
15
29
110
19'
1-3
66
105
37
57
105
35
123
210
35
0.51
81
55
19
31
25
8
112
80
14
Subtotal
169
285
100
115
300
100
284
585
100
< 0.5
5335
190
40*
511
50
14*
5846
140
29*
Total
5504
475
100
626
350
100
6130
825
100
*Percent of the total.
7400
1200
BOO?
.70 ,;r1
o 480
r: 200? 3
CYCenter NW Urals Urals Central Siberia
(coal) (gas) Asia
Joint electrical energy systems
Fig. 1. Zones of economic efficiency of a CHPP (1); equal
efficiency (2); the efficiency of the separate scheme (ICES +
RBU) (3).
according to a graph of heat loads, the possibility of operation with extreme discharge or total shutdown
for prolonged nonheating period (up to 3000-4000 h/yr);
the lack of a need for circulating water and the possibility of placing them in the center of large popula-
tion masses (when using petroleum residue fuel gas);
the simplicity of operation, the small number of servicing personnel, and the relatively low level of
qualifications required of them.
Technoeconomic studies have shown that the decisive factor involved in choosing the type of source of
centralized heat supply using organic fuel (CHPP or boiler units) is the level of concentration of the heat loads.
Naturally, this level will be quantitatively different in the various regions of the country (Fig. 1) which have
different conditions of heat supply [5]. In terms of the level of concentration of heat loads and the required
(by the necessary conditions for reliable supply) number of units (nu =4-6 and more), the unit output of regional
boiler units is from 30 to 150-180 Gcal/h.
The Economic Prerequisites for the Establishment of Atomic Boiler Units. At higher specific capital
investments, atomic bOiler units (ABU) can be competitive because of their lower fuel components of reduced
expenditures on the production of heat compared with boiler units using organic fuel. The maximum permis-
sible investment on ABU depends on the cost of organic fuel, the fuel component of the reduced expenditures,
and the placement conditions. The data shown in Fig. 2 characterize the conditions for replacing ABU and
CHPP using organic fuel. For typical price levels of organic fuel during the period prior to 1990 (30-35 rubles/
ton ideal fuel) and realistic values of the fuel component of the reduced expenditures, unit investments on ABU
can be 2.5-5.5 times as large as those for boiler units using organic fuel.
If ABU are oriented toward additional heat loads above 400-600 Gcal/h, the economic conditions fortheir
construction must be determined by making a comparison with CHPP using organic fuel. Because of the higher
efficiency of the latter, the maximum possible unit investments on ABU are lowered. If we refer these to the
unit investments on boiler units using organic fuel, the maximum allowable excess of the unit investments on
ABU is between 1.5 and 5 times larger.
2
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a
70 u'
20
JO
40
0km
-0
20
SO
3
2"
x49
ruble/ ,
Gcal 1
3 2 7
0
20
25
SO
1 2 3
ii 5
/
/
1
35
4J1-
\
%
eo.f , ruble/ton ideal fuel
Fig. 2. Conditions for the economic competitiveness of
ABU: a) ABU replace CHPP; b) ABU replace RBU; 1-6)
the fuel component of the cited expenditures on ABU, equal
to 2, 1.8, 1.6, 1.4, 1.2, and 1 ruble/Gcal, respectively;
IABU, TRBU) the specific investment in ABU and RBU;
eu.f) closing expenditures on organic fuel; Aef) the differ-
ence between ABU and RBU of the fuel component of the
cited expenditures per unit of heat delivered to users.
The distance the heat is transported is indicated on the
curves.
Technical, Performance, and Economic Characteristics of ABU. Atomic boiler units can be established
on the basis of the familiar types of nuclear reactors (water-cooled?water-moderated power reactors (VVER),
RBMK, AMB, and VK), allowing for the possibility of reducing the coolant temperature at the reactor outlet
and the necessity for reducing their unit output. Atomic boiler units can also be based on specialized nuclear
reactors oriented toward ABU operating conditions. For example, they can be based on nuclear reactors cooled
by high-boiling organic liquids which have good potential for effecting pressure reduction in the reactor loop.
It should be noted that in every case the ABU will be quite different from organic-fuel boiler units on account
of the specific properties of the nuclear reactor as an energy source.
The structure and nomenclature of the necessary services and equipment (control and safety rods, gas
management, technical waste control and purification, supply and storage of fresh fuel, burial or transporta-
tion of radioactive waste, etc.) in the reactor section and fuel management of ABU is almost the same as in
the reactor equipment of atomic electric power plants and atomic central heating-and-power plants (ACHPP).
Unlike boiler units fired with petroleum residue fuel gas, ABU require much larger areas, to allow for the
disposition of the services and equipment noted above and a zone for purposes of health protection. Also, ac-
cess must be provided to these areas (most likely by railroad) in order to supply fresh fuel and remove the
spent fuel. This complicates the problem of locating the ABU in or near densely populated areas. The main-
tenance of ABU is not altogether clear at this time. They require a large number of highly qualified personnel,
and in order to be used only in their heat-supply capacity, must either be stopped or discharged down to 10-
20% of their nominal power for a nonheating period (3000-4000 h/yr). Analyses of actual data on condensing
atomic electric power plants and calculated figures for ABU (at the engineering proposal and design sketch
stage) have shown that the specific cost of reactor installations largely depends on their unit output, while the
constant component takes up 60-80% of the total expenditures on the production of heat by ABU.
Increasing the unit output of reactors and raising the utilization factor of their installed capacity thus
enhances the economic competitiveness of ABU much more than of boiler units using organic fuel.
The unit heat output of ABU (QAuBU) and their utilization factor are rigorously related to the attached
heat load (Qatt), the required number of units (nu), and the fractional participation of the reactors in the cover-
3
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ECHSS
'
7 2 3
i\
723 ?
?
_
? . ??.?
?
74 45 45 47 C15 49 aABU
_ABU
Fig. 3. Effect of or- on the specific reduced expendi-
tures on heat supplied to users in a CHSS for closing ex- "
penditures on organic fuel of 40 (1), 35 (2), 30 rubles/ton
ideal fuel (3) and fuel components of reduced expenditures
on ABU of 2 (?), 1.5 (---). and 1 ruble/Gcal (-?-?---).
age of the added heat load (a ABU). Increasing the utilization factor of the installed capacity (which is pos-
sible because of a reduction in the fractional, participation of the reactors in the coverage of the added heat
load) necessarily reduces the unit output of ABU reactors and vice versa. A decrease in aABU from 1 to 0.5
increases the annual number of hours of usage of the installed capacity of ABU reactors by a factor of 1.5
(from 3000-3500 to 4500-5000), and the unit output of the reactors is reduced by a factor of two.
The choice of a rational value for aABU is made by a process of technoeconomic optimization. Figure 3
shows the results of economic estimates which were made for a centralized heat supply system (CHSS). The
expenditures per unit of heat supplied to users are plotted vs aABU for a calculated regional heat load of 2000
Gcal/h and for various values of the cost of organic fuel and the fuel component of the cited expenditures on
ABU.* The result is that for CHSS based on ABU it is appropriate to include the peak reserve organic-fueled
boiler units, which considerably reduces the cited expenditures per unit of heat (ft13-10%). The optimal value
of aABU depends on various factors, such as the cost of organic fuel, the unit capital investment in peak re-
serve boiler units, the length of the transit network from the ABU to the centers of heat usage, etc. Calcula-
tions show that depending on the combination of these factors, the optimal value of aABU lies within the range
In order to make it possible to establish 500-1000 MW (the output of the power reactors of contemporary
atomic electric power plants is 3-6 times as much) in the structure of heating ABU with 2-4 units for a re-
actor with unit heat output, attached heat loads of from 1500 to 6000 Gcal/h are required.
These technical, operational, and economic characteristics of ABU make it doubtful as to whether they
can be considered as the direct analog of boiler units using organic fuel.
Economic Competitiveness and Use of ABU. The main factors which bear on the economic competitive-
ness of ABU are cost of organic fuel, attached heat load (which influences the unit output of ABU reactors and
their technoeconomic characteristics), disposition relative to centers of heat usage, length of the heat con-
ductors running to the points of heat usage, the fractional participation of the attached heat load, and the utiliza-
tion factor of the installed capacity.
Studies were carried out to determine the effect of these factors on the economic competitiveness of
ABU arid their usage; some of the results are plotted in Fig. 4. The figure gives a plot of the ratio of the max-
imum allowable and anticipated actual specific investments (i) in ABU, as a function of the attached heat load
(and the corresponding unit heat output of the ABU reactors), the cost of organic fuel, and the distance from
centers of heat usage.
For organic fuel costs below 40 rubles/ton ideal fuel, ABU are thus unable to compete with boiler units
which use organic fuel wherever the latter are employed (Qatt
100-600 Gcal/h), because the anticipated spe-
*The range assumed for the variation of the relative investment in ABU (allowing for their dependence on the
output of the unit) is indicated in Fig. 4.
4
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220
200
180
,c 160
co
("j140
Z1.1
? 120
t'S 100
'80
60
a
?
,
2
S..
2/I .
..-_ 3
40- Zone of Zone zone
RBU of RBU of CHPP
or CHPP
20 ,
100 209 490 600 1000
Qat" Gcal/h
40,
2000
4000
Fig. 4. Economic competitiveness of ABU, for completing
expenditures on organic fuel of 40 (?.?.?), 35 (---), and
30 rubles/ton ideal fuel (?), a, b) actual specific invest-
ments in the ABU; 1, 1', 1", 2, 2', 2", 3, 3', 39 maximum
allowable investments in ABU.
cific investment is more than the maximum allowable value. For the level of completing expenditures on petro-
leum residue fuel gas which is projected for the period up until 1990 (30-35 rubles/ton ideal fuel), ABU can
compete only with basic CHPP using organic fuel; ABU become competitive for attached heat loads of 1500
Gcal/h and above. This value is higher than the minimum allowable figure for ACHPP (1000 Gcal/h and higher),
since the unit heat output of the ABU reactors cannot be lower than 500 MW. Unlike boiler units using organic
fuel, which in CHPP provide a way of extending the application of centralized heat-supply sources at the ex-
pense of providing heat to smaller users, ABU using low-temperature nuclear reactors can only supplement
ACHPP in supplying heat to large users. Therefore, the factors which are crucial in deciding on the advis-
ability of their construction may restrict the choice of areas to accommodateACHPP in a given region (taking
into account the fact that they cannot be farther from the heat users then the economically admissible distance).
These factors may also hinder the economically appropriate introduction of electricity-generating powerbased
on the fact that ACHPP will have a large associated condensed output.
Rational disposition of the ABU with respect to heat users is an important factor in making the ABU eco-
nomically competitive. If ABU are located in the immediate vicinity of cities and areas of high population den-
sity, there will be higher specific expenditures on land confiscation, preparation of the surface, radiation safety
measures (compared with the existing norms for planning "remote" nuclear energy installation). If ABU are
located near populated areas, additional or reinforced protective shells may need to be constructed to prevent
ejection of activity into the surroundings, and it may be necessary to locate the reactor section underground
and construct additional facilities for treatment and transportation of radioactive wastes and spent fuel. Pre-
liminary estimates and an analysis of the variation of the economic characteristics of nuclear energy installa-
tions with their distance from centers of population show that construction and operating expenditures incurred
when ABU are located in the immediate vicinity of cities and populated areas may be 20-35% higher than the
alternative expenditures incurred when they are located at a distance of 15-20 km or more. Calculations taking
this into account show that in certain cases ABU with an overall attached heat load of 1500 Gcal/h and above
can be economically feasible and efficient when they are located 20-25 km from cities and large population
centers, in spite of the increased cost of the heat delivery networks. In this case the ABU continue to be com-
petitive with CCHP (see Fig. 4).
Atomic?Chemical Boiler Units Based on High-Temperature Reactors (HTR). As was noted above, one
of the most important ways to make nuclear sources of heat supply economically competitive (including ABU)
is by increasing the unit output of the nuclear reactors which enter into their structure. When liquid coolants
are used in heat transport systems, the possibilities for concentrating the heat outputs of ABU nuclear energy
sources are limited. The economically feasible limits to the distances of heat transfer using hot water in a
two-pipe system and assuming the possible elevation of temperature of the water in the supply mains of up to
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Fig. 5. Diagram of heat flow in an HTR atomic-chemical boiler unit:
1) device for steam-water conversion of methane; 2) heating of steam-
gas mixture; 3) heating of methane; 4) steam generator; 5) condenser;
6) regenerator; 7) methanator; 8) boiler (steam generator); -- --)
H2 +CO mixture; -X -X -) H2 +CO +H20 mixture; ?) CH4; - ?? - ? ?-)
CH4 +H20; -0-0) circulating water and process steam, ? ? ? )
water and water vapor.
180-200?C are about 30-40 km; for a single-pipe system they are 50-70 km. Heat in the form of steam can be
transported over distances of as much as 10 km, but this does not allow for centralization of the heat supply of
relatively small heat consumers who are separated from each other by distances of more than 100 km. In
order to fit nuclear heat supply sources (primarily ABU), it therefore would be useful to explore qualitatively
new heat-transfer systems which would be designed for economically efficient heat transfer over distances of
100 km or more. This problem may possibly be solved by using systems in which the transfer is accomplished
with "cold" heat-transfer agents, which transport the heat in a chemically bound state. As an example, such a
heat conductor could be composed of a gaseous mixture of H2, CO2, and CO, which can be obtained by the endo-
thermic vaporous conversion of methane [6]. A gaseous mixture (H2 +CO2 +CO) is transported in the cold form
along a pipe to the heat-usage centers, where methane is exothermally synthesized from H2, CO2, and CO in
special devices (methanators). The heat liberated in the reaction at temperatures as high as 400-650?C can
be used to supply heat to residential and industrial users. The methane cooled in the process of heating the
circulating heat conductor is sent to a conversion center. Since steam-water conversion of methane is ac-
companied by the absorption of large quantities of heat at temperatures of 850-900?C, the source of energy
for the conversion center must be the HTR (Fig. 5).
Preliminary estimates show that heat in a chemically bound state can be transported with economic effi-
ciency from nuclear conversion centers to heat-usage centers located over 100 km away. This creates new
possibilities for concentrating heat outputs and enlarging the unit outputs of the nuclear energy sources of an
atomic-chemical boiler unit by providing a large number of relatively small users with a centralized heat
supply (Qatt =100-600 Gcal/h).
ABU for Heat Supply to Underdeveloped and Remote Regions. The experience of successfully op-
erating the Bilibinsk ACHPP (which has three 36-MW central-heating power units) with a total design heat
output of 75 Gcal/h as well as experience with the ARBUS and VK-50 installations indicates that it is possible
to construct reliable and economically efficient low-power (5-100 MW) atomic heat-supply systems (based on
channel and box-type nuclear reactors cooled by boiling water and organic liquids. Along with combined heat-
supply installations (ACHPP), in some cases it may be useful to construct special-purpose atomic heat-supply
systems (ABU) for underdeveloped areas and regions with difficult access. Studies have shown that under the
conditions of fuel supply which prevail in these regions, ABU can be competitive if their specific investments
are not more than 22-25 times those of boilers using organic fuel. As shown by preliminary estimates of the
specific costs of ABU, such conditions can be ensured for unit nuclear reactor outputs in the several megawatt
range. At the present time a design has been worked out for an organic- organic reactor with 15 MW of heat
output (the ATU-15 system) for ABU.
CONCLUSIONS
? Together with ACHPP, atomic boiler units can in this way be effectively applied to centralized heat-
supply systems. In the European part of the country, a centralized heat supply to relatively small consumers
of heat cannot be achieved with ABU based on the types of reactors which have been perfected. This is not the
case with boilers using organic fuel. Atomic boiler units can supply heat mainly to large users (more than
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1500 Gcal/h) and particularly to regions where it is impossible or unfeasible to construct ACHPP. In under-
developed and remote areas, atomic boiler units can be economically efficient with nuclear reactors
operating at heat outputs levels of several megawatts. With the successful development and perfection of high-
temperature nuclear reactors and systems for transporting heat in a chemically bound state, the outlook is
that atomic?chemical boiler units will be created which will permit nuclear energy resources to be much more
widely applied as efficient centralized heat supply sources for smaller heat users, whose share of total heat
consumption is as high as 40%.
LITERATURE CITED
1. L. A. Melent'ev, Teploenergetika, No. 11, 6 (1976).
2. B. B. Baturov et al., Proceedings of the IAEA International Conference
Cycle, Salzburg, May 2-13, 1977, IAEA-CN-36/338.
3. G. B. Levental' et al., Teploenergetika, No. 11, 14 (1974).
4. L. A. Melent'ev, Optimization of the Development and Management of Large Power
Vysshaya Shkola, Moscow (1976).
5. B. V. Sazanov, A. I. Korneichev, G. V. Ivanov, and I. D. Sobol', in: Transactions of
tific -Research andDesign Institute of the Energy Industry, No. 7, 27, Moscow (1975
6. K. Kugeler, M. Kugeler, H. Nieben, and R. Harth, in: Proc. IAEA Symposium "The
Helium-Heated Steam Reformers," Vienna, IAEA (1975), p. 341.
on Nuclear Power and Its Fuel
MULTICRITERIAL OPTIMIZATION OF THE DEVELOPMENT
OF NUCLEAR POWER IN THE FRAMEWORK
OF THE PERSPECTIVES OF COMECON
Systems [in Russian],
the All-Union Scien-
).
Development of
V. N. Bobolovich and N. A. Trekhova UDC 621.039.003
The nuclear power of the COMECON member-countries composes an intricate system. On the one hand,
national programs for nuclear power development form a basis for predicting the nuclear power development
of the COMECON countries as a regional system; on the other hand, these programs are drawn up by taking
into consideration the demands placed on the COMECON nuclear power system. Such a system approach to
national economic tasks makes it possible to bring out the effect of socialist collaboration in the area of nuclear
power ?the effect of integration.
In view of the large number of factors affecting the development of the COMECON nuclear power system,
its future is hard to predict because of difficulties related to its dynamics and the multistage character of its
processes, its multilevel and hierarchic structure, the uncertainty of its conditions and parameters and the
choice of optimization criteria.
The choice of such criteria (goal functions) for the solution of optimization problems involved in study-
ing the structure of nuclear power in perspective leads to the so-called multicriterial optimization. The tran-
sition to the latter also comes from the attempt to estimate a property of solutions assumed from different
standpoints. The structure of developing nuclear power can be simultaneously optimized according to several
criteria by applying the method used to solve multicriterial problems.
Multicriterial problems arise in the following situations [1] (see Fig. 1):
a) an object is regarded as a single element with several criteria;
b) an object consists of several elements which are optimal according to one criterion;
c) an object can contain many elements, each being in a multicriterial situation.
The differences in these situations (one multicriterial element, many single-criterial elements, and many
multicriterial elements) is basic, because the methods used in the solution of one case are not applicable to
another.
Translated from Atomnaya Energiya, Vol. 46, No. 1, pp. 9-13, January, 1979. Original article submitted
April 24, 1978.
0038-531X/79/4601-0007$07.50 0 1979 Plenum Publishing Corporation
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Aobo d/oc
Fig. 1. Situations which lead to multicriterial problems.
? ) elements; 0) criteria.
Until now, the optimization of the development of nuclear power engineering within the scope of COMECON
has been carried out according to only one minimizing criterion ? the integrated requirements for natural
uranium. This was due to: 1) the importance of such a criterion for this new and important branch of energy
engineering, just beginning to come into use; 2) the fact that there were no theoretical principles in the eco-
nomics of nuclear power engineering (the first article in this area [2] was published in 1969); 3) the fact that
the COMECON countries did not have a common currency, which is now the trade ruble.
In order to make a more complete study of the effect of the various factors on our concepts of the pos-
sible outlook for the development of nuclear power engineering with mathematical modelling, economic criteria
such as reduced expenditures can also be used.
Application of the methods of solution for multicriterial problems to nuclear power engineering makes
it possible both to combine these most important optimization criteria (integrated requirements for natural
uranium and reduced expenditures), and to take into account other criteria (labor costs, costs of metal, etc.)
as well.
In solving multicriterial problems, one looks for such a solution which would be optimal for the set of
goal functions f ={f1} (i =1,2 M). In the majority of cases, however, no such solution exists simultaneously
for all fi. Therefore, a solution of a multicriterial problem is understood to be such a solution which may not
be optimal for any of the goal functions, but which is the most acceptable for the whole set of goal functions.
Such a solution of the multicriterial problem is called a compromise.
We now consider those problems of the structure of nuclear power engineering in which the methods of
multicriterial optimization find important application.
Problem 1. To optimize the nuclear power engineering structure of the COMECON member-nations as
a unified system, according to two criteria: that of minimum expenditure on natural uranium, and that of mini-
mum reduced expenditures in conversion rubles. This corresponds to the "one multicriterial element" situ-
ation. Constraints are imposed on imports of generating machinery, on electrical power out, and on the dis-
tribution of plutonium.
Problem 2. In optimizing the future structure of nuclear power engineering, it must be kept in mind
that by 1990, after which time the large-scale introduction of breeder reactors is expected, large quantities
of plutonium will be required.
The problem is therefore solved with the following goal functions: minimum expenditure on uranium,
minimum reduced expenditures, and maximum plutonium operating time. Constraints are imposed on generat-
ing machinery imports and electrical power output. This situation is that of "one multicriterial element."
The solution of such a problem for a 40-50-yr forecast will make it possible to bring out the role of
breeder reactors more fully and to show the necessity of their development within the structure of nuclear
power engineering in the framework of COMECON.
Problem 3. On account of such factors as the large scale of nuclear power engineering, the construction
of a large number of industrial nuclear power stations and the opening up of new types of nuclear power sta-
tions, and the necessity of cooperation between COMECON member-countries in the construction of individual
nuclear power plants, a number of problems are encountered in studying the future of nuclear power engineer-
ing. These relate to the mechanical-engineering base, expenditures on metals, and labor costs. It is there-
fore appropriate to optimize the structure of nuclear power engineering according to the following criteria:
minimum reduced expenditures, minimum expenditures on metals, and minimum labor expenditures. In this
case we meet the most complicated situation, that of "many multicriterial elements."
Problem 4. In solving the first two problems, one optimizes the structure of the nuclear power engineer-
ing of the COMECON member-countries as a whole. In studying the structure and perspectives for the develop-
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ment of nuclear power engineering separately for each country, it is useful to optimize the structure of nuclear
power engineering (regarding the nuclear power engineering of the COMECON countries as a unified system)
at first according to minimum expenditure in each country, and at the next stage according to minimum total
expenditure in the system. This corresponds to the situation of "many single-criterial elements." Constraints
on imports of industrial machinery to each country are imposed on the elements. The plutonium balance equa-
tions provide a relation between the elements. The solution of such a problem is of great interest in relation
to the study of strategies for developing nuclear power in COMECON countries.
The methods that are used effectively in solving multicriterial problems include the method of the lead-
ing target function, the generalized goal function, and the method of successive relaxations. Other methods
exist which are also used to solve multicriterial problems. These, however, do not correspond as well to the
problems of optimizing nuclear power development.
Method of the Leading Goal Function [3]. This specifies, as its name implies, the optimization of the problem
according to one goal function. The other goal functions are considered as additional constraints during the
separate steps of the calculations, which are done by the simplex method. The multicriterial problem thus
reduces to the traditional single-criterial one. We will apply this method to multicriterial problems with
linear goal functions and linear constraints. It can be used in solving Problem 3.
A variant of the leading goal function method is the Radzikovskii method [3], in which the optimization
according to each criterion is stipulated at the first step. As an example, we consider a three-criterial prob-
lem. Let the optimal values of the criteria be fg fg f? (for the sake of definiteness, we will assume them to
be maximal in the optimization with respect to each of them separately). We select the most important cri-
terion, e.g., f3. The optimal values obtained for the remaining criteria are compared with given quantities
Di and D2. At the next step, we carry out an optimization with respect to the most important criterion f3, with
the additional constraints
D012 > ? ? ? > fm?
For the sake of simplicity, we will assume that all of them must have a maximum value. The following is an
algorithm for finding the compromise solution. An optimal solution according to one criterion fi is found first.
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A certain "relaxation" Afi is assigned next. This determines the loss which it is possible to yield according
to this criterion in order to obtain a better result according to the next most important criterion f2. We now
find the optimal solution according to the criterion f2 with the additional constraint
fi(x)f7?Al?
where fPis the optimal value of fi.
Next, we again designate a relaxation Af2 which determines the loss from the optimal value of the second
criterion obtained in solving this problem, in order to then obtain the optimal solution of f3, etc.
The method of solution of multicriterial problems can be used for arbitrary goal functions with arbitrary
constraints. But we cannot apply this method directly in a number of cases because of difficulties which arise
which are related to the solution of optimization problems in which additional constraints are taken into ac-
count. It should be noted that in using the methods indicated, it is necessary to assign a "weight" to the goal
functions or to make preferences among them according to their importance. For this it is useful to apply
the methods of expert estimates [6], this being particularly important in such a new .field as nuclear power
engineering because they make it possible to include the practical experience, knowledge, and intuition of
specialists in formulating correct models of the behavior of a system.
The most widely used methods for making expert estimates are the method of preference and the method
of rank.
In the method of preference, the experts distribute the given criteria according to their decreasing im-
portance, determining the position of each criterion.
Let Rij be the position of the i-th criterion as determined by the j-th expert. Then the weighting coeffi-
cients of the criteria are determined by the expression
n
az = Rij, C: Ri.
i= 1771
where m is the number of criteria and n is the number of experts.
In the method of ranks, the expert estimates the importance of the criterion on a quantitative scale run-
ning from 0 to 10. The weighting coefficients of the criteria are in this case determined by the expression
m n
F wo,
j=1
where =Ti; (71; ts.the rank of the i-th criterion given by the j-th expert).
Let us consider a variant of the nuclear power engineering system of the COMECON countries: Bulgaria,
Hungary, the German Democratic Republic, Poland, Rumania, the USSR, and Czechoslovakia. We will solve
optimization problem 4 with a common store of the plutonium produced and with economic criteria. We will
thoroughly discuss the solution of this problem by the method of total relative losses. The choice of the method
is determined by the linearity of the goal functions and the constraints, the comparative simplicity of the cal-
culations, and the possibility of using goal functions of various dimensionality. The generalized goal function
and the goal functions of each of the COMECON member-countries can be represented either in the national
currency or in trade rubles.
The following constraint is introduced for this problem [7]; The balance equation of the input power for
each country
where i =1, M (M is the number of COMECON member-countries); xf,T,i, quantity introduced to the
i-th country during time T of the output of a nuclear power station of type f; NT,i, necessary growth during
time T of the output of all nuclear power stations in the i-th country.
In this variant, the structural connection between the nuclear power station outputs introduced into the
different countries is expressed by the equation for the balance between the secondary nuclear fuel ?plutonium
(the uranium?plutonium cycle is considered in the present problem) and the requirement of its breeder re-
actors and the operating time accrued by all of the nuclear power stations. This condition can be formulated
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in the following way: At each instant of time, the plutonium store of the system which is ready for loading
into the breeder reactors must be nonnegative.
We introduce the following notation: Fa, set of nuclear power station types using uranium as fuel, Fb,
set of nuclear power station types using plutonium, gik,T, specific yield of plutonium on the initial loading of
the nuclear power stations (per unit installed capacity l with fb reactors of the type (fb E Fb) introduced in the
time interval T; gf specific plutonium yield per unit of electrical energy produced in time T; gfbo-, specific
expenditure on plutonium per reloading per unit of electrical energy produced in time T; rb, inertia of the ex-
terior fuel cycle, i.e., the time between unloading the fuel elements to their loading after processing in the
reactor; aT, store of plutonium ready for loading which is available in the system up to the end of the interval
T; hf,i,T, annual number of hours of usage of the output of nuclear power stations of type f in the j-th regime
during the interval T; and GT _ Iv plutonium produced in the interval T rb by existing nuclear power stations
at the beginning of the reference period.
We consider two operating regimes of nuclear power stations: with the least possible number of hours
of usage in the first year of the introduction of output a =1) and with the least possible number of hours of
usage (j =2) in the following years of operation of the nuclear power stations. In the first year of operation
of nuclear power stations with breeder reactors, the fuel expenditure per reloading is equal to zero. The
quantity of plutonium produced by all types of nuclear power stations in the interval r is determined by the
equation
n a r-rb M
Pr = Gr- ? 7 7
rb 17-11 j1.71 T1 21
The quantity of plutonium loaded in nuclear power stations of the f-th type introduced in the interval r is
equal to
M
P?,.=
fbEFbi=1
The expenditure on plutonium per reloading in the interval r is determined by the equation
2 r-1 M
= \-1 gf ;
t1 21 b. b? ? b. ?
The condition for the nonnegativity of the store of commercial plutonium in the system is obtained in
the form
15r? Pr ar-t ar = 0,
r=r0, R'.
Here we use the economic criterion expressed in its monetary form, it being the one which most fully
answers to the problem posed in this study:
E1= S' (I C f 1 + are CI)
T
where ared is a nom for reducing the nonsimultaneous expenditures; If,t,t, investment in nuclear power sta-
tions of the f-th type in the year tin the i-th country; and Cf,t,i, cost of operating nuclear power stations of
the f-th type in the year t in the i-th country.
The first stage of the solution consists in solving the problem M times for each country without going
beyond the national scope; i.e., using constraints on the introduction of power to the given country and with
their own reserves of plutonium produced. This corresponds to the actual resources of each country. From
the minimization we obtain M optimal solutions which determine the optimal structure of nuclear power en-
gineering in each country.
At the second stage of the solution, we minimize the goal function, which is written for the entire system
as a whole as
E. Eo
e-
E
2=1
Such a form for the goal function ensures minimum deviations from the optimal national plans for de-
veloping nuclear power engineering in the COMECON countries, while making the goal function dimensionless
and enabling the Ei to be expressed in conversion rubles as well as in the national currency.
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In case it is necessary to give preference td a particular country because it is desirable to make it the
location of a large number of a certain type of nuclear power station, preference coefficients pi are inserted
into the goal function. These can be determined by the "expert" methods.
In this case, the goal function is
Ai- I
E ?E ?
E E pi
E i9
i=I
E?
I
In conclusion, it should be noted that multicriterial optimization problems, like all optimization problems,
should be solved not by just one but by several methods owing to the lack of an adequate mathematical model
for the problem of an actual national economy. Therefore, the solutions obtained must be multivariant in assess-
ing their features by means of the assumed solution.
LITERATURE CITED
1. M. A. Aizerman, Avtom. Telemekh., No. 5, 83 (1975).
2. V. V. Batov and Yu. I. Koryakin, Economics of Nuclear Power Engineering [in Russian], Atoniizdat, Mos-
cow (1969).
3. V. L. Volkovich, in: Cybernetics and Computational Methods [in Russian], No. 1, Naukova Dumka, Kiev
(1969), p. 44.
4. V. L. Volkovich, in: Complex Systems of Equations [in Russian], Naukova Dumka, Kiev (1969), p. 100.
5. E. S. Venttsel,, An Introduction to the Study of Operations [in Russian], Nauka, Moscow (1964).
6. R. Echerrode, Manage. Sci., 12 3 (1965).
7. A. D. Virtser, G. B. Levental,, and S. Ya. Chernavskii, At. Energ., 33, No. 6, 955 (1972).
AN ESTIMATE OF THE UNCERTAINTY FACTOR
FOR PREDICTING THE DEVELOPMENT OF NUCLEAR
POWER ENGINEERING
S. Ya. Chernavskii UDC 621.311.2:621039 +
001.57 +519.283
Experience has shown that the use of mathematical modeling is the most effective way to forecast the
development of nuclear power engineering. A model which takes into account the economic criteria of a sys-
tem has been developed [1, 2] for making long-range forecasts. The model introduces: a) a set of linear con-
straints of the form
Ax= b, x>0, (1)
(where x is the desired strategy for development of the system; A, a matrix; and b, constraint vector) and b)
the linear functional being minimized in region (1), with
cx min, (2)
where c is the specific expenditures vector.
The desired strategy x is found for given A, b, and c by one of the methods of linear programming.
Known models [3-8] with specific characteristics have the same mathematical statement of the problem
(equivalent to the problem of linear programming) as in expressions (1) and (2). A characteristic of any linear
programming model is its determinacy, i.e., the single-valuedness of all exogenetic data of the model which
enter into A, b, and c.
However, the situation encountered in forecasting nuclear power engineering is such that many important
characteristics are not known with precision. Since they cannot be precisely known, in modeling they are repre-
Translated from Atomnaya Energiya, Vol. 46, No. 1, pp. 13-19, January, 1979. Original article submitted
April 6, 1978.
12 0038-531X/79/4601-0012$07.50 ?1979 Plenum Publishing Corporation
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sented in an inexact form, usually in the form of intervals of possible values. Several factors determine the
uncertainty of the characteristics; e.g., the instability of the object studied (this appears, in particular, in the
ambiguity in the directions of technical progress), the limited nature of the knowledge process, the psychologi-
cal nature of the persons who are the sources of the forecasts, etc. In the present problem the uncertain fac-
tors are the investment in fast-reactor nuclear power plants, cost of mining and reserves of natural uranium,
the rates of long-term growth of nuclear power, the dates for bringing fast reactors into operation, etc. Under
conditions of uncertainty, it is therefore not possible to apply the optimization criteria in the form of expres-
sion (2). The attempt to overcome this defect of the model of linear programming is multivariant, but using
determinate data in calculations is of little help [9]. In most cases this uncertainty results in ambiguous fore-
casts for the structure of nuclear power engineering and makes it necessary to develop a different method-
ological basis and a different way of optimization which takes the uncertainty into account.
It should be noted that the values of the majority of the factors which are represented in an indeterminate
form at the time of prediction are not formed by a random mechanism. This pertains, e.g., to such indicators
as natural uranium reserves, the dates for putting commercial fast reactors into operation, the investment in
them, etc. Since the uncertainty does not reduce to randomness in the problem of forecasting the structure of
nuclear power engineering, it is not appropriate to use stochastic programming methods [10].
It has also been pointed out [8] that the factors which most strongly affect the structure of nuclear power
engineering are concentrated in the vector c, i.e., in the coefficients of the functional of the determinate op-
timization problem. These factors are the investment in nuclear power stations with fast and thermal reactors.
We will consider this case of optimization under conditions of uncertainty, with the vector b and the matrix A
given in determinate form, and the vector c given in an indeterminate form. We shall refer to the problem of
finding the optimal strategy in an indeterminate situation specified in this way as a problem of the first kind
[11].
Solution of the Problem of the First Kind. Let the set of allowable strategies for development of a sys-
tem of nuclear power engineering be given by Eqs. (1). Let there be also given the set D of possible values
of the vector c. It is assumed that it is impossible to control the choice of any vector c, i.e., the existence of
the set D reflects the incompleteness of the knowledge of the character of the future development of the sys-
tem, on the one hand, and the objective indeterminacy of the development of the system at the time of prog-
nosis, on the other hand. In such a situation it is impossible to use directly criterion (2) of minimum reduced
expenditures, since it has no meaning for set D. It is further assumed that D is a convex set. The method
described in [11] does not operate with a continuous set, but with a discrete subset of vectors et, c2 cs
of this set. Henceforth, the set of limiting points will be used as the discrete set. It is proven that by dis-
cretizing the convex set D by its limiting points, and applying a method proposed in [11] to this discrete set,
one can determine the strategies that are optimal on the whole set D. In light of the above, a method for taking
the indeterminacy into account is characterized in the following way.
1. The method of optimization: For the optimization criteria, we use the set of criteria of the theory of
statistical solutions, viz., the criteria of Wald, Savage, Laplace, and Hurwitz. According to the Wald criterion,
one calculates a strategy which in comparison with every other has the least expenditure under the worst con-
ditions defined on the set D which are possible for the given strategy. According to the Savage criterion, a
strategy is found with the least maximal risk. According to the Laplace and Hurwitz criteria, strategies are
found with the least average and least weighted expenditures, respectively. In the last case, the minimal and
maximal expenditures are "weighted" by a coefficient which is specified a priori and which is a constant for
each country.
2. The optimal strategy is determined on the whole set of allowable strategies (see Eq. (1)) and on the
whole set of possible values of the vector c ? the set D.
3. No arbitrary rejection of part of the data occurs when this method is used, nor is nonessential data
included unjustifiably (e.g., on reducing the indeterminacy to randomness).
4. The method is oriented toward the linear programming approach.
The following order of steps in the calculations is recommended.
First Stage. Using a specially developed method, the work is organized to formulate the exogenetic data
of the model.
Second Stage. A separation is made between the essential and nonessential data, consistent with the
goals of the calculation. The basis of the separation can be past experience, expert estimates, or special cal-
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TABLE 1. Parameters of Special Linear -Problems in Allowing for the Factor of Inde-
terminacy
,
Criterion
Formula of the
criterion
Linear functionals
Constraints No, of linear/No, of
problems /constraints
Mean expendi-
tures (Laplace)
Max. expendi-
tures (Wald)
Max. risk .
(Savage)
Weighted expen-
ditures for a
given a ? of the
expenditure
(Hurwitz)
_
. s
(1/S) 2 (ci, .)
i=1
max (ci, x)
21 .....S 8
max [(ci. x)?zi]; zi=
=min (cix)
x:Ax=b
a min (ci., x)d-(1?a)x
i
X max (ci, x)
s
(1/S) min ( 2 ei, x)
min y
min y
..,
mi.n K; K =
2
=min [(ac, x) +
=1, 2, ..., S
Ax -= b; x> 0
Ax=b; y,--?;-.: (c?', x);
i = 1. 2. ..., S;
x ..>.(1; y .::, 0
Ax=b; y ...> (ci, x)?
?zi; i=1, 2,..,., S;
x .",, 0; y 0
Ax=b; (c1, x) < (ej,
x); j=1, 2, ...,

Y (ek, x); k = 1,
2, ..., S; x > 0;
1:m.
1, m ? S
S+1/m+S
S:111+25-1
culations based on a linear programming model. Nonessential parameters in the subsequent calculations are
represented by mean values. The essential parameters, which are given by a range of values, form a convex
set (in the process, the interdependence of the essential parameters should be taken into account, consistent
with the specification of the problem). Instead of the continuous set, the set of peaks of the convex set of the
essential parameters is selected for subsequent calculations.
Third Stage. For each peak ci, the following problem is solved on the linear programming model with
constraints (1): the linear functional cix is minimized. The purpose of this stage is to find the numbers zi =
min ex.
Fourth Stage. The special problems of linear programming are formed and solved in accordance with
Table 1 [11]. The purpose of this stage is to find the set of the optimal strategy of development under the con-
ditions of indeterminacy.
Fifth Stage. The optimal strategies found are analyzed, taking into account the specific content of the
problem being solved. The purpose of this stage is to narrow down, as much as possible, the recommended
strategy.
Sample Calculation. The structure of nuclear power engineering was calculated for 50 years. The effects
of the indeterminacy of the specific investments in nuclear power stations with fast and thermal reactors and
the cost of mining natural uranium were studied. Each of them was defined initially as a range of possible
values and the set together constituted a convex polyhedron. In accordance with the method used, the
polyhedron was replaced by the set of limiting points. Each limiting point, conventionally designated by a
state of the medium, is characterized by three numbers: If and rt are the investments in nuclear power stations
with fast and thermal reactors, and Cnat is the cost of mining natural uranium. The characteristics of the
peaks of the set D, which formed the calculated set of states of the medium, is shown in Table 2 (maximum and
minimum values are denoted by bars above and below respectively).
We consider fast breeder reactors, fast-converter reactors, thermal reactors using enriched uranium,
and thermal reactors which will be converted to plutonium fuel in the middle of the 21st century. Converter
reactors are reloaded with uranium only during the first 3 years, and then are converted to a breeder regime.
The hypothesis that the regime of reloading such reactors is efficient has been confirmed [9]. It has been pro-
posed that fast reactors will be put into service by the beginning of the 1990s and at that time will be widely
introduced in power engineering (the model distinguishes between the concepts of possibility and advisability:
The optimal time for introducing breeder reactors on a wide scale is determined on the model, i.e., is an endo-
genic variable). Possible improvements in technology were taken into account in assigning the reactor char-
acteristics. The thermal reactors considered were of the light-water type.
Each peak of the set was assigned a number for which is used the following notation; 1.1, 1.2, 1.3
1.8. We also refer to the peaks of the set D as limiting states.
Along with the exact method for optimizing under conditions of indeterminacy, which is considered here,
other, less accurate methods for determining the optimal strategy are also possible. According to the simplest
and least accurate method (but which has become widely used; see, e.g., [12]), the optimal strategies are deter-
mined from the number of strategies found on a linear programming model; i.e., from the number of strategies
14
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Declassified and Approved For Release 2013/02/12 : CIA-RDP10-02196R000800010001-5
TABLE 2. Variants of the States of the Medium ?the Peaks of the Set D
State
IndicatorIndicator
Date of putting nuclear power stations
into service
Rel. cost of mining natural
uranium, by categories
1986?
1990
1991?
1995
1996?
2005
after
2005
1
2
3
1.1
1.2
'
1.3
1.4
1.5
1.6
1.7
1.8
Ff
_
It
_
If
_LI
If
It
fi
la
If
_
It
If
It
If
It
If
It
--
325
--
325
--
265
--
265
?
325
--
325
?
265
?
265
440
325
440
325
440
265
440
265
355
395
355
325
355
265
355
265
330
270
330
270
330
220
330
220
315
270
315
270
265
220
265
220
265
245
265
245
265
190
265
190
235
220
235
220
215
190
215
190
'-riat
Coat
Gnat
Cnat
--nat .
C
. nat
ETnat
Slat
1
0,75
i
0,75
1
0,75
1
0,75
1,76
1,32
1,76
1,32
1.76
1.32--
1,76
1,32
2,4
2,4
2,4
2,4
2.4
2,4
2,4
2,4
in the third stage. In our work, this approximate method was used to determine to what degree application of
the more precise method would be justified. The approximate method can be termed a first-approximation
method, and the strategy obtained with it can be said to be optimal in the first approximation.
In order to distinguish the first-approximate strategies, we used the designations of those corresponding
limiting stages with which the present strategies were determined, enclosing the designation of the strategy in
double brackets. For example, (( 1.1)) denotes a strategy found by optimizing the linear programming model
under the assumption that the limiting state 1.1 is realized. Similarly, a strategy which is optimal on the linear
programming model with the limiting state 1.2 is denoted by ((1.2)). In conformity with this, eight such strategies
are defined; ((1.11, V.2)), q1.8). Four characteristic values were calculated for each of them: the max-
imal expenditures and risks, and the average and weighted-average expenditures. The development strategies
which were optimal in the first approximation were then chosen in accordance with the four criteria used under
the conditions of indeterminacy. A subsequent analysis and calculations showed that all of the strategies 41.14,
(1.2)) 41.8)) have the following basic properties;
fast reactors are present in all optimal structures of nuclear power engineering for the calculated period;
from a certain stage which is characteristic for each strategy, fast reactors begin to displace thermal
reactors;
from the beginning of the 21st century, thermal reactors are gradually converted to plutonium fuel;
the increase in the cost of mining natural uranium, which was used in the calculations, is a more important
factor than the uncertainty of the mining cost within the categories; the latter uncertainty did not appear to have
a long-term effect on the structure of nuclear power stations;
the ratio a of the investment in nuclear power stations using fast and thermal reactors has a significant
effect on the solution obtained in optimizing the date for which widespread construction of fast reactors is ini-
tiated.
With minimal E (the states 1.5 and 1.6), i.e., under the most economically favorable conditions for the
development of breeder reactors, the optimal date for introducing fast reactors would already have to be at
the beginning of the 1990s, and their share by the end of the century would come to about 30%. These data ap-
proximate the results which would have been obtained by optimizing the structure of nuclear power engineering
according to the criterion of minimum requirement for natural uranium. The share of thermal reactors using
enriched uranium would decrease by 1995 to 35% (by the end of the century to 7%), but the share of thermal
reactors using plutonium fuel would increase. Their share at the beginning of the 1990s would be 30%, and by
the end of the century would amount to 50%. By the beginning of the 2020s their share decreases to 15%. The
difference in the cost of natural uranium with respect to the first two categories of reserves in these states
does not have any effect on the structure of nuclear power engineering.
15
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Declassified and Approved For Release 2013/02/12 : CIA-RDP10-02196R000800010001-5
TABLE 3. Matrix of Expenditures and Criterial Values
Strategy
Expenditures
Numerical value of the criterion
1.2
1.2
Medium state
1.3 1.4 1.5
1.6
1.7
1.8
Wald Laplace Hurwitz
Savage
Optimal accord, to the
first-approximation
method:
85,8
85,0
79,7
78,8
82?3
81,3
72,0
72,5
85,8
79,5
73.9
2,6
#1.2#
86,1
84,8
79,5
78,5
82,3
81,3
72,2
71,0
86,1
79.5
74,1
2.4
t1.3*
88,4
86,9
77,6
76,1
85,7
84,1
75,1
73,5
88,4
81,0
76.4
4,4
41.4)i
88,4
86,9
77,6
76,1
85,7
84,1
75,1
73,5
88,4
81.0
76,4
4,4
(4.5?
86,9
86,0
81,9
81,0
81,7
80,9
72,6
51,7
86,9
80.4
74,8
4,9
d.6*
87,0
86,0
81,9
81,0
81,7
80,9
72,6
71,7
87,0
80,4
74.8
4.9
85,8
85,0
79,8
78,8
82,3
81,3
72,0
74,0
85,8
79.5
73.9
2.6
(4.8*
86,0
85,0
79,5
78,5
82,3
81,3
72,0
71,0
860
79.5
73,9
2.4
Optical accord to ex- -
act method-oftakin&un-
certainty into account:
?Idald)?
85,-8
85,0
79,7
78,8
82,3
81,3
72.0
71.0
85,8
'
79.5
73.9
2,6
86,0
73.9
?>
86,0
85,0
79,5
78,5
82,5
81,4
72,0
71,0
86.0
79,5
73,9
2,4
3; 3) the statistical approach for calculating perturbations is concurrent in the
sense of expenditure of machine time and the use of computer resources, even in two-dimensional problems
in the case where the diffusion approximation is applicable; 4) it is most efficient to use difference iterations
to estimate reactivity effects from local perturbations, allowing for distortion in the source distribution.
21
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Declassified and Approved For Release 2013/02/12 : CIA-RDP10-02196R000800010001-5
The above concept of difference iterations emerged from stimulating disoUssions of the idea With M. N.
Nikolaev, Ya. V. Shevelev, A. D. Frank-Kamenetskii, and L. V. Maiorovti. The author thanks all of them for
their serious interest.
LITERATURE CITED
1. M. Gubbins, AEEW-M 581, Winfrith (1966).
2. T. Hoffman and L: Petrie, Trans. Am. Nucl. Soc., 15, 912 (1972).
3. M. Berger and J. Dogget, NBS J. Res, 56, 89 (1956).
4. G. A. Mikhailov, Zh. Vychisl. Mat. Mat. Fiz., 7, No. 4, 915 (1967).
5, V. G. Zolotukhin, in: Progress in Reactor Physics [in Russian], No. 1, FEL Obninsk (1968), p. 140.
6. H. Takahashi, Nucl. Set. Eng., 41, 259 (1970).
7. W. Matthes, ibid., 47 234 (1972).
8. L. N. Usachev, in: Reactor Engineering and Theory [in Russian], Izd. Akad. Nauk SSSR, Moscow (1955).
9. D. Irving, Nucl. Eng. Des., 15, 273 (1971).
10. V. F. Khoklov, M. M. Savos,kin, and M. N. Nikolaev, in: Progress in Atomic Science and Engineering,
Series: Nuclear Constants [in Russian], No. 8, Pt. 3, TsNII Atominform (1972), pp. 3-132.
11. V. V. Korobeinikov et al., ibid.,No. 18 (1975), pp. 85-155.
12. D. A, Usikov, Preprint FEI-423, Obninsk (1973).
13. M. N. Zizin, L. N. Kudryashov, and M. N. Nikolaev, Preprint NIIAR P-4 (270), Dimitrovgrad (1976).
14. A. D. Frank-Kamenetskii, Preprint IAE-2416, Moscow (1974).
15. I. G. Timofeev and A. D. Frank-Kamenetskii, Preprint IAE-2526, Moscow (1975).
CORROSION PRODUCTS IN MAIN TECHNOLOGICAL
SYSTEMS OF ATOMIC POWER PLANTS
WITH AN RBMK-1000 REACTOR DURING OPERATION
V. M. Sedov, P. G. Krutikov,
E. A. Konstantinov, A. V. Shultgin.
V. I. Ryabov, Yu. 0. ?Zakharzhevskii,
A. P. Eperin, and V. G. Shevchenko
UDC 621.311.25:621.039
? The chemical conditions of the system of an atomic power plant are determined by the set of specific
properties of the aqueous working medium and of the structural materials, the operating conditions, and their
reciprocal influence. Analysis of the chemical conditions in the technological system consists of an evaluation
of the corrosion state of the materials of the system and observations of the parameters of the aqueous medium.
The present paper is devoted to a study of the corrosion state of the surface of structural materials of
the systems and equipment of an atomic power plant with an RBMK-1000 reactor. In the study samples were
taken directly from the system (during the operation of the atomic power plant) and from the outer surface of
the equipment (during shutdown after 21,000 h of operating at power). The samples of deposits were taken in
five segments (Table 1) of the main circuit of the atomic power plant (see Fig. 1): in the drum-separator, in
the multiple forced-circulation circuit (MFCC), in the steam circuit (steam pipes, high- and low-pressure
cylinders (HPC and LPC)), and in the condensate-decontamination circuit (deaerator, mechanical filter).
The chemical isotopic and phase composition were determinedinorder to identify the compounds in the
samples (Tables 2 and 3). Techniques for determining the chemical composition were described earlier [1, 2].
The phase composition of low-activity deposits was determined on a URS-50 NM x-ray apparatus with an SSD
stand and the phase analysis of the radioactive deposits was made by the -y-ray resonance method on a YaGRS-4
spectrometer [3, 4].* The spectra were taken in a transmission geometry in a constant rate mode. The en-
*For more details of the technique and some results of this analysis, see the paper by A. I. Moskvin et al.,
(this issue, p. 27).
Translated from Atomnaya Energiya, Vol. 46, No. 1, pp. 23-28, January, 1979. Original article submitted
April 7, 1978.
22
0038-531X/79/4601-0022 S07.50 ?1979 Plenum Publishing Corporation
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Declassified and Approved For Release 2013/02/12 : CIA-RDP10-02196R000800010001-5
TABLE 1. Characteristics of Sampling Segments
Site of deposit sampling Material of equipment
Medium and its parameters
Drum-separator*
"Shade flowmeter
EFPTt
Steam pipes emerging
from drum-separator
HPC, third stage
HPC, fifth stage
Deaeratort
Mechanical feedwater
filter
*Surface area 230 m2.
t280 m2.
t 165 m2.
Steel 22K, EI-898
(plating)
Khl8N1OT
Khl8N1OT
Grade 20 steel
Rotor 43KhM1A
steel, vane 1Kh13
steel, diaphragms
OKh13 steel
Ditto
Walls grade 3 steel,
end plates grade
20 steel
Body grade 20 steel,
filter cartridge
steel Kh17N13M3T
Desalinated water, steam?
water mixture (moisture
content 14-17%), steam
(moisture content 0.1%),
p = 2 7 MPa, t =284.5?C
Desalinated water, p =7 MPa,
t=(5 2 280?C
Desalinated water, t= 50-
70?C, contact with nitrogen
p =0.15 MPa
Steam (moisture content
0.1%), t =280?C,
13=5.5 MPa
Steam, p =0.53 MPa, t =160?C
Steam, p =0.35 MPa, t =138?C,
moisture content 15.9%,
p =0.6 MPa, t =164?C
t =165?C
Fig. 1. Diagram for sampling deposits from equipment
of atomic power plant with RBMK-1000 reactor: 1)E FPT;
2) separators; 3) mechanical filters; 4) emergency feed
pump; 5) TsEN-7 pumps; 6) bypass decontamination; 7)
HPC; 8) separators?steam preheaters (SSP); 9) LPC; JO)
condensers; 11, 13) condensate pumps CPI and CPU;
12) condensate decontamination; 13, 14) low-pressure
preheaters; 15) deaerator; 16) electric feed pumps;
? ) sampling site.
23
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Declassified and Approved For Release 2013/02/12 : CIA-RDP10-02196R000800010001-5
TABLE 2. Chemical and Phase Composition of Loose Corrosion Products from Surfaces
of Equipment of RBMK-1000 Reactor
?
Sampling site ,
. .
Phase composition,
. wt.%
.
Chemical composition,
wt. 10 in sample
.
n-
oluL'i
le
eSi -
ue
Fe304
y-Fe203
a-Fe203
y-Fe0OH
Fe
Cr
Ni
Mn
Cu
Zn
Si
Drum-separator (from
control samples)
54
46
-
49.7
1,85
1,8
1,23
0.07
-
-
-
Drum-separator (from
bottom of apparatus)
-
-
-
44.6
1,64
0.52
0.43
0.43
0.13
-
18.9
EFPT
-
-
-
46.2
1.65
0.6
0.6
0.3
0.1
-
4.0
Suspensions in coolant
(from drum-
separator)
30
-
70
-
-
-
-
-
-
-
-
-
Steam pipes of drum-
separator
30
-
70
-
65.0
0.09
0.014
0.56
0.14
0.078
0.003
-
Steam pipe before ? .
check-regulating
valve
-
-
100
-
60.3
0,32
0.12
0.49
0.1
.,?
04
-
-
Diaphragm of third
stage of HPC
-
100
-
67.8
0.13
0.006
0.011
0.07
0.091
0.7
-
Steam pipe of HPC-
15
15
70
-
67,3
0.088
0.059
0.014
0.085
0.20
1.6
-
SSP (at steam outlet
from fifth stage of
HPC)
Steam pipe of HPC -
SPP:
upper layer of de-
posits (black)
lower layer of de-
posits (cherry_
colored)
70
-
-
30
100
-
-
73,6
68.1
0.03
0.1
-
-
0.004
0.003
-
-
-
-
-
-
-
-
LPC, at steam outlet
from fifth stage
(black)
70
20
-
10
60.5
0.1
-
0.17
-
-
-
-
LPC, at steam outlet
from fifth stage
(reddi,sh-brown de-
posits)
-
-
100
49.2
0.05
-
0.64
-
-
?
-
Suspension from con-
densate decontamina.
39
15
17
24
60
0.3
0.05
0.3
3.4
-
-
-
Deaerator tank
28
30
42
-
66.4
0.09
0.05
0.013
0.016
0.002
-
-
Mechanical feedwater
filter
7-
-
100
-
65.9
0.27
0.1
0.13
0.01
0.1
-
TABLE 3. Radiochemical Composition of Corrosion Products, Ci/g
Rad ,ionu-
cliue
Sampling site
drum-sepa-
rator (from
bottom of
,
apparatus)
steam pipe
ahead of
of check- HPC (ahead
regulating
valve)
from dia-
phragms of
HPC
steam pipe of
HPC -SSP at
steam outlet
from fifth
stage of HPC
steam pipe
after LPC
deaerator
Niechan.
filter
f or feed-
water de-
contamin.
31Cr
s4Aln
39Fe
48C0
60Co
65Zn
05Zn
35N9
103Ru
1089u
3.36cs
131Cs
140Ba
141Ce ,
144Ce
Total
(9,4?1,3)? 10-4 - (8,0,-2,8)? 10-8
(2,2?-0,7)? 10-5 - -
- - (9,2?3,8)'10-3
(4,4?0,9)? 10-5 - (5,0?2,8).10"9
(7,2?0,9)? 10-5 (5,1?3,3)? 10-10(1,4?0.3). 10-s
(9,4-_,_- 1,7)? 10-5 - (2,5?0,6)? 10-8
(0,7?0,5)? 10-4 - (2,4 _,t0,7)? 10-8
(9,1?0,9)? 10-4 (3,0?0,9)? 10-4 2,94?1,7). 10-8
(4,1,2)'103 - -
(4,7?0,9)? 10-4 - -
- - -
- -(2,7?1,6)? 10-9
- - -
(2,1 ?0,9)? 10-3 - 6,3?0,8)? 10-3
(9,5?4.8)15-4 - -
(4,1?0,2)?10-3(2,6?0,1)? 10-8(4,9?0,3).10-7
?
-
(4,7?2,8).10-0
-
-
(2,4?0 ,/,)? 10-8
(3,7?0,8)? 10-s
(2,8?0,6)? 10-8
(5,6?0,8)?10.-s
-
-
-
-
-
(1,7?0,3)? 10-8
(1,2?0,2)?10-7
(3,6?0,3).10-7
- (1,9?0,3)-10-s
- (9,7?_1,1)?10-0
- (2,2?0,0).109
- (1,9,-0,5)? 10-4
- (1,7,0,2)? 10-3
- (0,1?1,2)? 10-3
(2,8?1,8)? 10-0 (2,7?0 ,p)? 10-0
(3,0?2,0)? 19-9(6.2?1.1). 10-4
- -
- (7,4?3,7)? 10-3
- (1,3?0,8)? 10-9
(1,2?0,7)? 10-3 -
(1,2?0,5)? 10-8 (7,5?1,4)? 10-9
- (8,5?1,0)? 10-9
(7,2?0,3)? 10-9 -
(5,9?0,0)? 10-8 (1,7?0,1)? 10-7
-
(1,5?0,7)? 10-7
-
(1,9?0,9)? 10-1
(3,5?-0,7)? 10-7
(4,5?2,0)? 10-7
(1,1?0,2)? io-6
(2,0?0,3).10-8
(1,8?1,1)- 10-1
(2,0?0,7)? 10-6
-
-
-
(2,5?1,0)? 10-7
(3,2?0,5).106
(1,2?0,1)? 10-1
ergy spectrum of the deposits was recorded with a DGDK-40 semiconductor detector with an intrinsic resolu-
tion of 2.7 keV for the 1332-keV y line of 60Co with an AI-4096-ZMV-100 analyzer. The spectra were analyzed
on an M-6000 ASVT by procedures described earlier [5].
The data from visual examination of equipment surfaces are given in Table 4. The GTsN delivery pipes
displayed corrosion damage in the form of pits and pockholes up to 2 mm deep, situated along the periphery
in the region of weld seams. The pockholes are coated with a dense oxide film ranging from light brown to
black in color; blackoxides also appear at places where the surface of the pipes has been treated mechanically
24
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Declassified and Approved For Release 2013/02/12 : CIA-RDP10-02196R000800010001-5
TABLE 4. Corrosion Condition of Equipment Surfaces
Equipment
Characteristics of surface condition
Drum-separator
"Shade flowmeter
EFPT
Steam pipes of drum-separator
Steam pipe before check-regulating
valve
Steam pipe (receiver) of HPC ?SSP
(4 m from fifth stage of HPC)
HPC
LPC
Deaerator
Mechanical feedwater filters
Surface of manhole cover has no damage after removal of loose de-
posits. The bulk of the corrosion products on the bottom of the ap-
paratus.
Covered with dense, thin, gray and black film tightly adhering to metal.
Considerable quantity of dark brown deposits on bottom of tank. Tank
walls are 70% covered with loose corrosion products, located mostly in
the region of weld seams.
Surface completely covered with fine pits up to 7 mm in diam. and up
to 0.5 mm in depth. Waterlines appear in horizontal segments of pipes.
Surface of lower part damaged more intensively than surface above
waterline. Most large pits on surfaces of pipes are in lower part.
Superficial brown deposits adhering tightly to surface of metal. No
visible flaws can be seen on surface after removal of deposits.
Dense two-layer superficial deposits on walls of steam pipe. Upper
layer consists of black corrosion products which flake off in scales of
up to 0.2-0.3 mm thick. The cherry-colored bottom layer adjoining the
metal reaches a thickness of 0.5 mm. The surface under the deposits
has no visible corrosion damage.
When the loose brown deposits are removed the steam pipe leading to
the HPC shows no visible damage. Surfaces of steam pipes and dia-
phragms of HPC are smooth, without traces of corrosion damage. The
packing segments and their mounting springs are covered with dense
black oxide films coated with a loose brick-covered red deposit. The
vanes of the first and second stages are covered with pockholes and
pits as a result of metal erosion. The vanes of the fourth and fifth
stages have a dense oxide film on the side opposite to the steam flow.
At the steam outlet from the HPC the surface of the steam pipe and
guide vanes are covered with pits of different shapes with even vertical
edges, diam. of 2 to 20 mm, and depth of up to 1 mm. At the bend in
the steam pipe (with a change in direction of flow) the surface is shiny,
as if glazed.
The surface of the turbine housing is covered with loose deposits rang-
ing from reddish brown to black in color. The surface of the trailing
edges of the rotor vanes is honeycombed with numerous pits and spots.
In the deaerator tank a waterline dividing the steam and water phases
appears on the walls at a distance of 0.2 diam. from the bottom. Below
the waterline the surface is reddish brown, monochromatic, and com-
pletely covered with pits and spots up to 1 mm in diam. and 0.5 mm in
depth. Above the waterline there are loose brick-red deposits under
which fine spots and pits with a diam. of 2-3 mm are observed. The
condition of the weld seams does not differ from that of the surface of
the tank walls. The surfaces of the deaerator column, delivery steam
pipes, and grids are coated with dark (greenish-violet iridescent)
dense oxide film.
The filter covers, housing walls, and guide vanes of filter cartridges
are covered with brick-colored corrosion products. Pits with a diam.
of up to 1-2 mm appear on the surface of the cover when the loose de-
posits are removed. There are very many corrosion spots, as a result
of which the surface is rough. The stainless steel parts bear no traces
of corrosion damage.
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A considerable quantity of loose corrosion products accumulated in the drum-separator of the MFCC,
concentrated primarily on the bottom of the separator; the walls were coated with a thin layer of deposits.
The surface of the manhole cover had no visible damage (after removal of the loose deposits). The emergency-
feed pump tank (EFPT) had up to 70% of its surface covered with loose corrosion products. When the steam
parameters in the-steam circuit are reduced the composition of the loose corrosion products changes. Thus,
two-layer deposits are observed even in the HPC; the blackish upper layer is a mixture of magnetite and hema-
tite whereas the lower layer consists only of hematite (see Table 2).
According to the data from electrochemical polarization measurements [6], the continuous film on the
housing of the "Shadrft flowmeter (MFC circuit) has a spinel composition: (Fe, Ni)0-- (Fe, Cr)203. The loose
corrosion products from the bottom of the drum-separator contain (in percent of weighed sample) 45-50 Fe,
up to 2 Cr, up to 0.6 Ni, and up to 0.5 Mn.
In systems of pearlitic steels (grade 20, grade 3, and grade 22K steels) the deposits are due entirely to
iron oxides (65-68%), those of other elements being 300?C goes over entirely
into a-Fe203. Hematite can also go over into the coolant from corrosion deposits on overheated surfaces [1].
In addition to the above-mentioned oxide compounds of iron, magnetite can also appear in the aqueous coolant,
e.g., by the Schikorr reaction [7]:
3Fe +41320-4- Fe304+81-1+.
(1)
Thus, the coolant of an operating reactor may be expected to contain Fe304 and a-Fe203 at a high temper-
ature and lepidocrocite and an intermediate form of its dehydration, maghemite, at a low temperature. The
phase composition of the corrosion products in the coolant of the drum-separator at 285?C and the condensate-
decontamination apparatuses at 30-40?C (see Table 2), found by the Massbauer-effect method, confirms the
validity of our assumptions.
As for the high-temperature corrosion deposits, with our sampling technique the composition of the cor-
rosion-product samples called loose deposits may prove to contain corrosion products formed on steel of the
external epitaxial layer of the protective corrosion film [8]. Moreover, it may also contain particles of corro-
sion deposits carried by coolant or steam from other parts of the circuit as well as hydrolysis products of
ionic forms of iron, formed in the coolant itself. The tightly adhering deposits on grade-20 carbon steel may
presumably consist of oxide compounds formed on the surface of the protective corrosion film consisting of
an inner (topotaxial) and an outer (epitaxial) layer [8]. This may in part receive magnetite particles which
are tightly bound up with the metallic surface; this magnetite is formed when the metal reduces the deposited
hematite [1]:
Fe +4a = Fe203-4-
(2)
In the case of stainless steels a protective film is built of ferritic or chromium?nickel spinels with the
general formula AB204, where A are ions of divalent metals (Fe2?, Mn2?, 7n2+, Ni2+,...) and B are ions of
trivalent metals (Fe3+, Cr3+, A13+,...) [8]. The protective film on carbon steel (depending on the oxygen con-
tent in the coolant) consists of either magnetite (or maghemite) in the pure form or successive layers Fe304?
y-Fe203?Fe304 [1, 9]. The superficial deposits, as a rule, consist of a mixture of magnetite and hematite [1].
Under our conditions one would expect magnetite, maghemite, and hematite in the loose deposits and magnetite
and maghemite in tightly adhering deposits on grade-20 steel. It is seen from Table 2 that in actual fact this
assumption holds only for loose deposits in the deaerator. The presence of only y-Fe203 in loose deposits on
the assembly in the coolant of the drum-separator is evidently due to the fact that only the dehydration products
or lepidocrocite from the coolant enter these deposits. Bearing in mind that the transport of particles by the
steam is much smaller than that by the coolant [10], the similarity of the composition of the loose deposits on
stainless steels in the steam?water phase of the coolant and in the system for extraction of live steam can be
attributed to the local origin of these deposits. Unfortunately, with the sampling technique employed, bits of
the metal surface enter the tightly adhering deposits, in spite of the protective film formed by the oxides (Fe304
and T-Fe203); this explains why the Massbauer spectra of the tightly adhering deposits contain the lines of
metallic iron (see Fig. 1). The presence of hematite in the tightly adhering deposits may be due to the incom-
plete oxidation of Fe304 to a-Fe203 [1].
It has thus been shown that M8ssbauer spectroscopy can be used to determine the phase composition of
iron compounds in the activated corrosion products of the structural materials of the RBMK-1000 primary
circuit. The phase composition of the oxide forms of iron depends on the temperature of the circuit segment
from which the samples of corrosion products were taken.
LITERATURE CITED
1. 1. K. Morozova et al., Transport and Deposits of Corrosion Products of Reactor Materials [in Russian],
Atomizdat, Moscow (1975).
2. H. Leidheiser et al., Chem. Acta, 45, No. 1, 257 (1973).
3. M. Graham and M. Cohen, Corrosion, 32, No. 11, 432 (1976).
30
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4, W. Meisel, Werkstoffe Korros., 21, 249 (1970).
5. W. Meisel, in: Prof. Fifth Intern. Conf. on Mossbauer Spectroscopy, Part 1, Bratislava, Sept. 3-7 (1973),
p. 200.
6. T. Misawa, Corros. Set., 13, 659 (1973).
7. G. 33onsack, Mitt. VGB, 51, No. 11, 61 (1971).
8. H. Kirsch, WerkstoffeKorros., 22, No. 6, 527 (1971).
9. K. A. Nesmeyanova et al., Teploenergetika, No. 1, 54 (1976).
10. A. P. Veselekin, M. A. Lyutov, and Yu. E. Khandamirov, At. Energ., 24, No. 3, 219 (1968).
ACTIVITY OF RADIONUCLIDES IN THE COOLANT
OF THE SECONDARY LOOP OF A NUCLEAR POWER
PLANT WITH VVER-440 REACTORS
L. M. Voronin, A. P. Volkov,
V. F. Kozlov, L. M. Luzanova,
and V. I. Pashevich
UDC 621.039.584
Radionuclides in the water and steam supplied to boilers and turbines by a nuclear power reactor present
a certain radiation hazard. As a result of small defects in the piping, cooling water in the primary loop can
leak into the water and steam of the secondary loop.
We have used data from the Kola nuclear power plant. The first unit of this plant operated more than 3
years before January, 1977 and the second unit more than 2 years. the first unit generated 5.2.109 kWh of
electrical energy (520 effective days) during two runs, and the second unit generated 3.0.109 kWh (298 effective
days) during one run.
Each VVER-440 commercial type reactor in the Kola nuclear power plant operates with six steam gen-
erators (SG) which supply steam to two turbogenerators (TG). The pressure of live saturated steam in the secondary
loop reaches 4.7 ? 106 N/m2 at 260?C, and the circulation of water is 2700 tons/h. The pressure of the coolant
in the steam generators in the primary loop is 12.5 ? 106 N/m2 at an average water temperature of 282?C.
After passing through the high-pressure cylinder (HPC) and two low-pressure cylinders (LPC) of a turbo-
generator the spent steam enters the condensers. After passing through two heating stages and a deaerator
the condensate returns to the steam generators (Fig. 1).
To remove contaminants,partof the water at a flow rate of 15-16 tons/h is drawn from the steam gen-
erators and passed through a special purification unit (SVO-5).
The total volume of water in the secondary loop is -1250 m3, including 106 m3 in 10 low-pressure con-
densate heaters (LPH), 240 m3 in two deaerators, 600 m3 in two condensers, and 256 m3 in six steam generators.
As a result of bleeding off steam for in-plant needs, the loss of water through leaks in the secondary
loop and the water sampler, the discharge of steam through expansion tank vents, the circulation system ejec-
tors and various excess pressure relief valves, the secondary loop has to be supplied chemically desalted
water at the rate of -20 tons/h through the condenser. Half of this loss is from steam consumed for tech-
nological needs.
Thus, the replacement fraction of the volume of water in the secondary loop is 20/1250=1.6 10-2/h.
As a result of the irrevocable loss of water and the use of fresh water the coefficient ni characterizing the
removal of nongaseous radionuclides from the water is half this value, i.e.,
ni 0.8.10-2 h1.
The water in the secondary loop is further freed of radionuclides by the Eon-exchange filters of the water
purification unit (SVO-5). Lithe radionuclides were completely trapped by these filters the decontamination factor n2
would be 15/1250=1.2-10-2/h.
Translated from Atomnaya Energiya, Vol. 46, No. 1, pp. 31-35, January, 1979. Original article submitted
September 30, 1978.
0038-531X/79/4601-0031 $07.50 1979 Plenum Publishing Corporation 31
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0
Steam to
TG2
Steam header
HPC 1>/./0 LPC1 LPC2
--r,__
,,'7`,.
Spent Turbine
steam Ejectors ejector gases
-0?
Feed header
From turbogenerator 2
high-pressure heaters
HPH
8
0.2.2
o
LPHLLPH_LPH_LPH?LPI-1.__,??_
HPH HPH
7 6
Deaerator gases
r Fig. 1. Activity of radionuclides in coolant of secondary loop of a nuclear power plant.
TABLE 1. Average Values of Measured Concentrations of Certain
Radionuclides in the Water of the First and Second Units of the Kola
Nuclear Power Plant, Ci/liter
Radionuclide
First unit
Second unit
primary loop
boiler water
primary loop
boiler water
uNa
5,9.10-5
< 1.10-12
1,6.10-5 < 1.10-12
42K
7,6.10-6
a a
1,2.10-6 a a
18F
1311
5,6.10-6
6,1.10-6
a ),/
5,2.10-11
1.0.10-6a H
5,0.10-5 8,9.10-11
1331
3,3.10-5
4.4.10-14
1,5.10-4 8,1.10-11
422/
2,9.10-5
?
1.1.10-4 --
8574Kr
2,0.10-5
Not observed
9,0.10-5 ' Not observed
88Kr
3,0.10-5
The same
1,1.10-4 The same
138Xe
2,8.10-4
a a
2,1.10-8 a a
185Xe
1,8.10-4
a a
6,4.10-4 a a
Total activity
of gasee
5,1.10-4
a a
2.8.10-8 a a
Notes. 1) From dosimetry monitoring data the total activity of gases
in the exhaust of the turbine ejectors is less than 5 ? 10-1? Ci/liter on
the average, but sometimes increases to 2 -10-9 Ci/liter. 2) Radiom-
etry data show that the average total activity of the dry residue of
boiler water on the steam generators is about 4.1 times smallerthan
the 1311 or 133I activities.
If we introduce a correction for the measured efficiency of trapping 1311 and 1331 entering the water of the
secondary loop together with radioactive gases, n2 is decreased to 0.7- 10-2/h. Gaseous radionuclides are not
retained by the water purification filters.
The accumulation and equilibrium content of a radionuclide in the water of the secondary loop is described
by the equation
dQldt= gA?(k+ Xr ni n2) Q, (1)
where Q is the activity in the water of the secondary loop, Ci; A, the concentration in the water of the primary
loop, Ci/liter; g, the rate at which water leaks from the primary into the secondary loop, liters/li; X, the decay
32
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TABLE 2. Calculated Leakages of the First
(gi) and Second (g2) Units, g/h
Radionu-
clide
X
ni
n2
gi
g2
1311
3,6.10-3
0,8.10-2
0.7.10-2
41
12
nai
3.3.160
0,8.10-2
0,7.1Cr2
17
7
Av.
value
29
9,5
constant and Ar is a constant describing the removal of activity With the steam. The deposition of 1311 and 133I
on the surfaces and equipment of the secondary loop can be neglected in view of the low value of the sorption
constant. The solution of this equation is
Q=(gAIX?Ar ni n2) [1- exp - (X Xr ni 712) t]. (2)
Under steady-state conditions for a constant leakage of the primary loop and a constant supply to the secondary
loop, Eq. (2) simplifies to
Q=gAIX-1--Xr +ni+n2. (3)
The unknown in Eq. (3) is g - the leakage of water from the primary into the secondary loop. The re-
maining parameters are monitored during the operation of the power plant and are known to a certain accuracy.
Table 1 lists the average concentrations of certain radionuclides in the water of the primary loop of both
units of the Kola nuclear power plant. The averaging was performed over a three-month interval preceding
shutdown for refueling and routine maintenance, i.e., toward the end of the run of each unit. The radionuclide
composition of the steam generator boiler water is presented for the secondary loop. The specific activity of
the dry residue of a sample of this water is generally 4 MeV. The correction for the background of accompanying reactions took account of the
fission of nuclei by neutrons from parasitic (p, n) and (d, n) reactions on molybdenum and titanium which enter
into the composition of the targets. The maximum number of 235U fissions by neutrons from accompanying
(p, n) reactions did not exceed 4.4-5% (E11=3.4 MeV), but reached 30% for (d, n) reactions. The corrections ,
of the 240pu/ 235u and 242p
U/23 5U fission cross-section ratios did not exceed 1.8-2.1% for (p, n) reactions (En5
3.4 MeV) and were 1.5-4.5% for (d, n) reactions (En=5.5-7.4 MeV).
39
In the second stage of the work the absolute values of the 240pu/239pu and 242pu /2 Pu fission cross-sec-
tion ratios were measured for En= 0.975, 1.5, 2.0, 2.5, and 3 MeV. The use of 239Pu instead of 235U in this
stage enabled us to apply the "method of isotopic admixtures" to determine the ratios of the numbers of fission-
able nuclei in the layers being investigated and in the reference layers. This method can be used when the
cross section under study has a threshold character. For example, highly accurate measurements of the ab-
solute values of the 238U/235U fission cross-section ratio were made in this way [1]. The main advantage of
the method is that while the work is proceeding at the accelerator both the ratios of the numbers of fission-
able nuclei in the layers, and the absolute values of the fission cross section ratios can be determined directly
Translated from Atomnaya Energiya, Vol. 46, No. 1, pp. 35-40, January, 1979. Original article sub-
mitted January 30, 1978.
0038-531X/79/4601-0035 807.50 O 1979 Plenum Publishing Corporation 35
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with an ionization detector. This eliminates the necessity of determining the absolute efficiency of the fission
chambers, and requires only a small correction for the change in the ratio of the chamber efficiencies as a
function of neutron energy.
In this part of the work layers of 240Pu and 242Pu containing 6.7 and 5.89 admixtures of_.239PU respectively
were specially prepared and subjected to careful mass spectrometric analysis. Layers of 239PU with an iso-
topic purity of 99.9% were used as standards. Under irradiation by slow neutrons with energies below the
240Pu and 242Pu fission thresholds, fission of 23913u nuclei was observed in the layers under investigation and
in the reference layers. The ratios of the fission rates by slow neutrons, in combination with the data on the
relative 239Pu content in the 240Pu and 242PU layers measured in the mass spectrometric analysis, permitted
the determination of the ratios of the numbers of fissionable nuclei in the 240pu/239pn and 242pu /239 Pu layers.
Since the slow neutrons induced 239Pu fissions in both the layers under investigation and in the reference layers,
the neutron spectrum can be arbitrary. Measurements were made in a flux of neutrons from the accelerator
target slowed down by a 10-cm-thick polyethylene block. The number of fissions produced when the detector
was covered with a 0.5-mm-thick layer of cadmium was subtracted from the number of fissions when the de-
tector was bare. The cadmium ratio was 18-20, and the corrections of the ratio of fission rates did not ex-
ceed 0.4-0.5%.
Measurements with slow neutrons were performed repeatedly with neutrons from the Li(p, n) and T(p, n)
reactions having maximum energies of 150 and 500 keV respectively. The agreement of the results within
1-1.5% showed that they are independent of the energy of the neutrons before moderation. To eliminate the
depression of the slow-neutron flux in the backing, the targets were irradiated alternately from both sides
to average the neutron flux through the layers.
After the measurements with slow neutrons a series of measurements was performed with fast neutrons
using the same layers and recording procedure. The combination of experiments with slow and fast neutrons
permitted the determination of the absolute values of the 240Pu/239Pu and 242Pu/239Pu fission cross-section
ratios for En= 0.975, 1.5, 2.0, 2.5, and 3 MeV. Since the 235U fission cross section was used as a standard
in the measurements of the energy dependence of the fission cross section ratios over the whole energy range
(0.127-7.4 MeV), the absolute values were also reduced to this standard by multiplying the 210Pu/239Pu and
242PU/238PU fission cross-section ratios by the value of af239Pu/crf235U obtained by the authors [2].
The values of the energy dependence of the 240pu/235u and 242Pu/235U fission cross-section ratios mea-
sured in the first stage of the work were normalized to the absolute values at the neutron energies indicated
above. In spite of the fact that the error of the absolute values in this method of calibration includes the un-
certainty in the 239Pu/235U fission cross-section ratio (1.4-1.5%), the "method of isotopic admixtures" is not
inferior in accuracy and is more reliable for 240Pu and 242Pu nuclei than other methods, such as the measure-
ment of the ratio of the a activities of layers.
Thus, the error in determining the ratio of the number of fissionable nuclei was determined largely by
the uncertainty of the 239Pu content in the 240Pu and 242Pu layers. Therefore the mass spectrometric analysis
of the specially prepared mixtures received particular attention. Isotopic analyses of the mixtures were per-
formed on samples of 10-8 g by counting ions and using the program of displacement of mass peaks. In pro-
cessing the results corrections were made for the background of scattered ions and isotopic discriminations
(by means of the accelerating potential and in the ion detector). The validity of the displacement of mass peaks
and the stability of isotopic discriminations were monitored by the rhenium ratio; Check experiments showed
no observable peaks of foreign materials with mass numbers from 239 to 242 and no affects of fractionation
in the evaporation process. The measurement of the 238Pu concentration was hampered by a small admixture
of 238u
present in the mixtures, and therefore an upper limit is indicated for the 239Pu content. Table 1 pre-
sents the results of the analysis, averaged over many mass spectra for various evaporation conditions. The
error indicated is the standard deviation. To increase the reliability of the data and to check the accuracy of
the corrections introduced, mixture 2 in Table 1 was analyzed independently on two mass spectrometers. The
two analyses agreed within the limits of error.
In the analysis of the mixtures an estimate was made of the content of 238U and nuclides with mass num-
bers 243 and 244. Their content was estimated as